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A new kind of method to solving solutions of the nonlinear coupling KdV equations. (Chinese. English summary) Zbl 1399.35322

Summary: In this paper, the problem of constructing the new infinite sequence complexion solution of the nonlinear coupled KdV equations is researched. With the help of the method combining the function transformation with the auxiliary equation, the new infinite sequence complexion solutions consisting by two of the Riemann \(\theta \) function, Jacobi elliptic function, hyperbolic functions and trigonometric functions of the nonlinear coupled KdV equations are obtained. These solutions conclude two-solitions, double-periodic solutions and soliton solution and periodic solution complexion solutions.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
35C08 Soliton solutions
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